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zysi [14]
3 years ago
7

Given: arc IV =140°, arc VK =30°, m∠ISV=135, Find: m∠VPL

Mathematics
1 answer:
ryzh [129]3 years ago
3 0

Answer:

The measure of the {\angle}VPL is 80^{\circ}

Step-by-step explanation:

We know that  the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

Now, Let

x is the measure of arc IV

and y is the measure of arc PK, then

m{\angle}ISV={\frac{1}{2}}(x+y)

Substituting the given values, we get

135^{\circ}={\frac{1}{2}(140^{\circ}+y)

270^{\circ}=140^{\circ}+y

y=130^{\circ}

Thus, The measure of arc PK is 130^{\circ}.

Also, we know that  the inscribed angle measures half that of the arc comprising , thus

Let

z is the measure of arc VK

and  y is  the measure of arc PK, then

m{\angle}VPL={\frac{1}{2}(z+y)

Substituting the values, we get

m{\angle}VPL={\frac{1}{2}}(30+130)=80^{\circ}

Hence, the measure of the {\angle}VPL is 80^{\circ}.

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Not sure how you want it; we'll do it in degrees. 

When we know the sine of an angle, there's usually two angles on the unit circle that have that sine.  They're supplementary angles which add to 180^\circ.  But when the sine is 1 or -1 like it is here, we're looking at 90^\circ and -90^\circ, which are essentially their own supplements, slightly less messy. 

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Check.  Let's just check one, how about

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